If you're getting interested in functional programming, you should really read John Backus' 1978 Turing Award paper, "Can programming be liberated from the Von Neumann style?", which was really seminal to the whole field. (I don't believe it's available to the general public on the web -- I couldn't find it -- but look for the August 1978 issue of Communications of the ACM.)

In spite of its age, the points it makes are still fresh and interesting. One of the main ideas, which you point out but don't really emphasize above, is that it's not procedural: your program doesn't say, "Copy these bits over there, then if that was zero, copy these others over here." It says something more like, "The result I want can be described like this." The main tool for describing the like this part are functions (in the mathematical and logical sense) and functional composition. (Hence the name. ;-)

In my experience, functional programming doesn't have a steep learning curve, but it does involve an "Aha!" experience. One day, it just starts making sense. Sorry, but I don't have a good way of getting you to that point, other than what you're doing. Like geometry, there is no royal road to non-procedural programming.